Finite Group Databasebeta

← #35307484

Subgroups — #35307484

Order 21248.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908435C212yesmaximal
2#24908282C211yesmaximal, characteristic
3#24905344C211yesmaximal, characteristic
4#24905344C212yesmaximal
5C83×#2845C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7C2×#14581715—22no—
8C2×#14581703C2212yes—
9C2×#14581703C2211yescharacteristic
10#19127463—22no—
11#19127463—22no—
12#398×C83—22no—
13#398×C83—22no—
14#398×C83—22no—
15#382×C83C2212yes—
16#382×C83C2211yescharacteristic
17C22×Dic166—21no—
18C22×C83⋊C8—21no—
19C22×C83⋊C8—22no—
20#14581792—22no—
21#14581792—21no—
22#14581792Q812yes—
23C2×C4⋊Dic83—22no—
24#14581715—44no—
25#14581703—22no—
26#14581703—22no—
27#14581703—22no—
28C2×C4⋊C4×C83—22no—
29C2×C4⋊C4×C83—22no—
30C2×C4⋊C4×C83—22no—
31C2×C4⋊C4×C83D412yes—
32C2×C4⋊C4×C83D412yes—
33C2×C4⋊C4×C83D412yes—
34C2×C42×C83C2311yescharacteristic
35#95×C83—22no—
36#95×C83—22no—
37#95×C83—22no—
38#95×C83—22no—
39C2×Dic166—22no—
40C2×Dic166—42no—
41C2×Dic166—42no—
42C2×Dic166—41no—
43C22×Dic83—41no—
44C2×C83⋊C8—24no—
45C2×C83⋊C8—22no—
46C2×C83⋊C8—41no—
47C2×C83⋊C8—42no—
48C2×C83⋊C8—42no—
49C2×C83⋊C8—41no—
50C4⋊Dic83—24no—
51C4⋊Dic83—42no—
52C22×C4×C83—22no—
53C22×C4×C83—22no—
54C22×C4×C83—22no—
55C22×C4×C83C2×D411yescharacteristic
56C22×C4×C83C2×D412yes—
57C4⋊C4×C83—42no—
58C4⋊C4×C83—42no—
59C4⋊C4×C83—42no—
60C4⋊C4×C83—82no—
61C4⋊C4×C83—82no—
62C4⋊C4×C83—82no—
63C42×C83C2×Q811yescharacteristic
64C42×C83#4112yes—
65C42×C83#4111yescharacteristic
66C23×C83#12011yescharacteristic
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—42no—
72C2×C4×C83—42no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83—42no—
76C2×C4×C83—42no—
77C2×C4×C83—42no—
78C2×C4×C83—42no—
79C2×C4×C83—42no—
80C2×C4×C83C22⋊Q812yes—
81C2×C4×C83C22⋊Q811yescharacteristic
82C2×C4×C83#12412yes—
83C2×C4×C83#12411yescharacteristic
84C2×Dic83—42no—
85C2×Dic83—81no—
86C2×Dic83—81no—
87Dic166—44no—
88Dic166—82no—
89C83⋊C8—42no—
90C83⋊C8—44no—
91C22×C83#39311yescharacteristic
92C22×C83#45311yescharacteristic
93C22×C83#45411yescharacteristic
94C22×C83#45512yes—
95C22×C83#45612yes—
96C4×C83—21no—
97C4×C83—21no—
98C4×C83—22no—
99C4×C83—22no—
100C4×C83—82no—
101C4×C83—82no—
102C4×C83—82no—
103Dic83—82no—
104#10361—831nomaximal, Sylow
105C2×C83#166112yes—
106C2×C83#166211yescharacteristic
107C2×C83#166311yescharacteristic
108C2×C83#202711yescharacteristic
109C2×C83#202812yes—
110#2845D8311yescharacteristic
111#1993—832no—
112#1960—831no—
113#1295—831no—
114#1295—832no—
115C83#1036111yescharacteristic, complemented, Sylow
116C2×C4⋊Q8—831no—
117C2×#103—1662no—
118C2×#97—831no—
119C2×#97—832no—
120#398—22no—
121#398—22no—
122#398—22no—
123#382C2×D8311yescharacteristic
124#382C2×D8312yes—
125#340—1662no—
126#340—1662no—
127C22×Q8—1661no—
128C22×C8—1662no—
129C22×C8—1661no—
130C4⋊Q8—832no—
131C4⋊Q8—1661no—
132C4⋊Q8—1662no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—1662no—
137C2×C4⋊C4C22⋊D8312yes—
138C2×C4⋊C4C22⋊D8312yes—
139C2×C4⋊C4C22⋊D8312yes—
140C2×C42C22×D8311yescharacteristic
141#103—3324no—
142#97—1662no—
143#97—1662no—
144#97—1662no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C2×Q8—3322no—
150C2×Q8—3322no—
151C2×Q8—3321no—
152C2×Q8—1662no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—3321no—
157C22×C4C2×C22⋊D8312yes—
158C22×C4C2×C22⋊D8311yescharacteristic
159C2×C8—3321no—
160C2×C8—3322no—
161C2×C8—3322no—
162C2×C8—3321no—
163C2×C8—1662no—
164C2×C8—1664no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—82no—
171C4⋊C4—3322no—
172C4⋊C4—1664no—
173C42Q8×D8311yescharacteristic
174C42#1305059112yes—
175C42#1305059111yescharacteristic
176C23#1458176111yescharacteristic
177Q8—3324no—
178Q8—6642no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—3322no—
193C2×C4—6641no—
194C2×C4—6641no—
195C2×C4#1458176812yes—
196C2×C4#1458176811yescharacteristic
197C2×C4#1458178112yes—
198C2×C4#1458178111yescharacteristic
199C8—3322no—
200C8—3324no—
201C22#1912761211yescharacteristic
202C22#1912786911yescharacteristic
203C22#1912787411yescharacteristic
204C22#1912787912yes—
205C22#1912788412yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—6642no—
214C2#2490678012yes—
215C2#2490678611yescharacteristic
216C2#2490679111yescharacteristic
217C2#2490861611yescharacteristic
218C2#2490862112yes—
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2845C2
socle, prime radicalC23×C83#120
hypercenter#2845D83
hypocenterC83#10361
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
115. C83#10361semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249084352
#249082822
#249053442
C83×#28452
#1036183